Inverted Pendulum Posture Control Using Energy Curve Eigenvectors
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Solution Overview
Problem
Conventional technologies face difficulties in controlling a height-variable non-linear inverted pendulum model due to the inability to obtain analytical solutions, necessitating iterative calculations.
Innovation Solution
A posture control method that derives a divergent component from an energy function without iterative calculation by converting a conservation energy function into a curve function and approximating eigenvectors as convergent and divergent components, using a control device to perform feedback control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional iterative calculation methods are used to control a height-variable non-linear inverted pendulum, then control accuracy can be achieved, but computational complexity and calculation time increase significantly
Solution Approach 1:
The invention transforms the control problem by changing the parameter representation from direct iterative solving to an energy-based parameter transformation. By converting the conservation energy function into a curve function and using eigenvector approximation, the method changes the mathematical parameters from iterative variables to analytically derivable energy parameters, thereby reducing computational complexity while maintaining control accuracy
Solution Approach 2:
The invention replaces the computational mechanism (iterative calculation system) with a mathematical transformation mechanism (energy function-based analytical solution). Instead of using computational iteration to solve the non-linear pendulum equations, the method substitutes this with an energy conservation approach that provides analytical solutions through curve function conversion and eigenvector approximation
2Reliability
If iterative calculations are performed for stabilization control, then stable control can be achieved, but real-time control performance deteriorates
Solution Approach 1:
The invention performs preliminary transformation of the control equations into an energy-based framework before actual control execution. By pre-converting the conservation energy function into a curve function and deriving the eigenvector relationships in advance, the method eliminates the need for iterative calculations during real-time control, thereby improving real-time performance while maintaining stabilization reliability
Solution Approach 2:
The invention extracts the essential control characteristics from the complex iterative system by isolating the energy conservation principle. By taking out the core energy-based relationship and representing it through curve functions and eigenvectors, the method separates the essential stabilization mechanism from the computationally intensive iterative calculation, enabling faster real-time control
Data Source
AI summary
A posture control method is a posture control method of a non-linear inverted pendulum model, of which a height of a center of gravity is variable, and a trajectory of the center of gravity is an energy conserving system, using a control device, the posture control method including: obtaining a conservation energy function on the basis of a measured value of the center of gravity; converting the conservation energy function into a curve function; and calculating a set of eigenvectors through approximation as a convergent component and a divergent component without iterative calculation of a controllable area in a phase plot of the converted curve function and feeding back the convergent component and the divergent component that have been calculated.